.. _slip-strength-slip-rule:

SlipStrengthSlipRule
====================

Overview
--------

These objects provide a relation between the stress, history, and temperature
and the slip rate on each individual slip system where the slip rate is related to the resolved shear stress on the system

.. math::
   \tau_{g,i} = \bm{\sigma} : \left(\mathbf{d}_{g,i}\otimes\mathbf{n}_{g,i}\right)

where :math:`\mathbf{d}_{g,i}` is the slip direction for group `g`, system `i` `in the current coordinates` and :math:`\mathbf{n}_{g,i}` is similarly the slip system normal.  The interface used is:

.. math::
   \dot{\gamma}_{g,i}, \frac{\partial \dot{\gamma}_{g,i}}{\partial \tau_{g,i}}, \frac{\partial \dot{\gamma}_{g,i}}{\partial \bar{\tau}_{g,i}} \leftarrow \mathcal{G}\left( \tau_{g,i}, \bar{\tau}_{g,i}, \bm{\alpha}, T \right)

   \dot{\mathbf{h}}, \frac{\partial \dot{\mathbf{h}}}{\partial \bm{\sigma}}, \frac{\partial \dot{\mathbf{h}}}{\partial \mathbf{h}} \leftarrow \mathcal{H}\left(\bm{\sigma}, \mathbf{h}, \bm{\alpha}, T \right)

where :math:`g` indicates the slip group, :math:`i` indicates the system within the group, and :math:`\bar{\tau}_{g,i}` is the slip system strength, defined by a SlipHardening model:

.. toctree::
   :maxdepth: 2

   ../SlipHardening

The definition of the history evolution is left to the SlipHardening model.

Implementations
---------------

.. toctree::
   :maxdepth: 1

   PowerLawSlipRule

Parameters
----------

.. csv-table::
   :header: "Parameter", "Object type", "Description", "Default"
   :widths: 12, 30, 50, 8

   ``strength``, :cpp:class:`neml::SlipHardening`, Slip hardening definition, No

Class description
-----------------

.. doxygenclass:: neml::SlipStrengthSlipRule
   :members:
   :undoc-members: